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1983 AHSME Problems/Problem 8

Revision as of 18:37, 26 January 2019 by Sevenoptimus (talk | contribs) (Slightly cleaned up and added more explanation to the solution)

Problem 8

Let $f(x) = \frac{x+1}{x-1}$. Then for $x^2 \neq 1, f(-x)$ is

$\textbf{(A)}\ \frac{1}{f(x)}\qquad \textbf{(B)}\ -f(x)\qquad \textbf{(C)}\ \frac{1}{f(-x)}\qquad \textbf{(D)}\ -f(-x)\qquad \textbf{(E)}\ f(x)$

Solution

We find $f(-x) = \frac{-x+1}{-x-1} = \frac{x-1}{x+1} = \frac{1}{f(x)}$, so the answer is $\fbox{A}$.

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